Optimal Control Of Diffusion Processes

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Optimal Control Of Diffusion Processes

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Author : Vivek S. Borkar
language : en
Publisher: Longman
Release Date : 1989

Optimal Control Of Diffusion Processes written by Vivek S. Borkar and has been published by Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Science categories.

Controlled Diffusion Processes

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Author : N. V. Krylov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-26

Controlled Diffusion Processes written by N. V. Krylov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-26 with Science categories.

Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. ~urin~ that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in Wonham [76]). At the same time, Girsanov [25] and Howard [26] made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4]. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8], Mine and Osaki [55], and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.

On The Optimal Control Of Diffusion Processes

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Author : Martin Lee Puterman
language : en
Publisher:
Release Date : 1996

On The Optimal Control Of Diffusion Processes written by Martin Lee Puterman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.

Controlled Markov Processes And Viscosity Solutions

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Author : Wendell H. Fleming
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-04

Controlled Markov Processes And Viscosity Solutions written by Wendell H. Fleming and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-04 with Mathematics categories.

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

Optimal Control Of Diffusion Processes

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Author : Wendell H. Fleming
language : en
Publisher:
Release Date : 1972

Optimal Control Of Diffusion Processes written by Wendell H. Fleming and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.

The paper summarizes some recent work on optimal control theory for continuous parameter stochastic processes. The author discusses only the control of Markov diffusion processes governed by stochastic differential equations of Ito type. Moreover, the author considers only the two cases when either: (A) no observations are available to the controller (open loop control); or (B) the states of the processes are completely observed by the controller. (Author).

Stochastic Control Theory

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Author : Makiko Nisio
language : en
Publisher: Springer
Release Date : 2014-11-27

Stochastic Control Theory written by Makiko Nisio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Mathematics categories.

This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.

Numerical Methods For Stochastic Control Problems In Continuous Time

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Author : Harold J. Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2001

Numerical Methods For Stochastic Control Problems In Continuous Time written by Harold J. Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Language Arts & Disciplines categories.

The required background is surveyed, and there is an extensive development of methods of approximation and computational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience."--BOOK JACKET.

Optimal Control Of Diffusion Processes With Discontinuous Coefficients

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Author : Keigo Yamada
language : en
Publisher:
Release Date : 1972

Optimal Control Of Diffusion Processes With Discontinuous Coefficients written by Keigo Yamada and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Markov processes categories.

Ergodic Control Of Diffusion Processes

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Author : Ari Arapostathis
language : en
Publisher: Cambridge University Press
Release Date : 2012

Ergodic Control Of Diffusion Processes written by Ari Arapostathis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.

Optimal Control Of Diffusion Processes And Hamilton Jacobi Bellman Equations

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Author : Pierre-Louis Lions
language : en
Publisher:
Release Date : 1983

Optimal Control Of Diffusion Processes And Hamilton Jacobi Bellman Equations written by Pierre-Louis Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.